Question

Students at Beloved Charter High School are tracking the growth of plants in biology. They discover that the plants growth is linear and want to predict how tall the plant will be after n weeks after the planting date. After the 2nd week of recording data, the plant was 4 inches tall. After the 5th week, the plant was 5.5 inches tall. a. Write an equation to represent the plant's height, h, in inches, n weeks after the planting date. b. How tall will the plant be in 10 weeks? C. After how many weeks will the plant grow to be 20 inches tall?

Answer 1

Given the information, we know that the groth is linear, and also we have two points: (2,4) and (5,5.5). Then we can find the equation in the following way:

`\begin{gathered} (x_1,y_1)=(2,4) \\ (x_2,y_2)=(5,5.5) \\ \text{slope:}_{} \\ m=(y_2-y_1)/(x_2-x_1) \\ \Rightarrow m=(5.5-4)/(5-2)=(1.5)/(3)=0.5 \\ m=0.5 \\ \text{ point-slope formula:} \\ y-y_1=m(x-x_1) \\ \Rightarrow y-4=0.5(x-2) \\ \Rightarrow y-4=0.5x-1 \\ \Rightarrow y=0.5x-1+4=0.5x+3 \\ y=0.5x+3 \end{gathered}`

If h are the inches and n the weeks, then the equation is:

`h=0.5n+3`

Now, if we want to know how tall will be the plant in 10 weeks, we just make n=10 and find the value of h:

`\begin{gathered} n=10 \\ h=0.5n+3 \\ \Rightarrow h=0.5\cdot10+3=5+3=8 \\ h=8 \end{gathered}`

therefore, after 10 weeks, the plant will be 8 inches.

Finally, to find out how many weeks will it take the plant to grow 20 inches, we make h=20 and solve for n:

`\begin{gathered} h=20 \\ h=0.5n+3 \\ \Rightarrow20=0.5n+3 \\ \Rightarrow20-3=0.5n \\ \Rightarrow n=(17)/(0.5)=34 \\ n=34 \end{gathered}`

therefore, the plant will be 20 inches tall in 34 weeks